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Efficient recursive canonical variate analysis approach for monitoring time‐varying processes
Author(s) -
Shang Liangliang,
Liu Jianchang,
Zhang Yingwei,
Wang Guozhu
Publication year - 2017
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.2858
Subject(s) - singular value decomposition , computation , computer science , algorithm , random variate , exponential function , covariance , matrix decomposition , mathematical optimization , mathematics , statistics , random variable , mathematical analysis , eigenvalues and eigenvectors , physics , quantum mechanics
Canonical variate analysis (CVA) has been applied successfully in process monitoring. This paper proposes an efficient recursive CVA approach to monitor time‐varying processes. The exponential weighted moving average approach has been adopted to update the covariance matrix of past observation vectors without the need for recalling past training data. The most important challenge faced by the recursive CVA algorithm is the high computation cost. To reduce the computation cost, the first order perturbation theory was introduced to update the singular value decomposition (SVD) of the Hankel matrix recursively. The computation cost of recursive SVD based on the first order perturbation theory is significantly less compared with conventional SVD. The proposed method is illustrated by the simulation of the continuous stirred tank reactor system. Simulation results indicate that not only can the proposed method effectively adapt to the natural changes of time‐varying processes but also the proposed method can also identify two types of abrupt sensor faults.